Question

the sum of two numbers is 55 their Hcf and lcm are 5 and 120. what are the two numbers?​

Answer 1

Step-by-step explanation:

Multiplication of two numbers is equal to multiplication of their hcf and lcm

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Answer 2

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★15 and 40

Explanation

Let a and b are two numbers.

a/c to question,

• a + b = 55 .---------(1)

• HCF {a, b} = 5

so, we can write a = 5k and b = 5l, where k and l are co-prime numbers.

putting a and b in equation (1),

• 5k + 5l = 55 => k + l = 11 -----------(2)

again, LCM{a, b} = 120

• so, 5 × k × l = 120

• k × l = 24 -----------(3)

from equations (2) and (3),

• k × (11 - k) = 24

• or, 11k - k² = 24

• or, k² - 11k + 24 = 0

• or, k² - 3k - 8k + 24 = 0

• or, (k - 3)(k - 8) = 0

hence, k = 3 and 8

putting in equation (2), l = 8 and 3

hence, if k = 3 then, l = 8

and if k = 8 then, l = 3

choose anyone of them,

• k = 3, and l = 8

then, a = 5k = 15. b = 5l = 40

hence, numbers are 15 and 40